One of the main lessons that we learned from string theory is that instead of working with a particular model (string or field), one should better consider families of similar models at once. This provides the most effective description of the problem, no matter has one to integrate over the space of theories (as in string theory) or not (as in the ordinary quantum field theory). This approach allows one to reveal various non-trivial structures underlying the family of theories that require involving a dynamics on the moduli space of theories. The most instructive examples of these structures are the algebras of constraints (Ward identities), that act on the partition functions of the theories [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]} and various integrable structures, from the standard integrability [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]} to the Whitham integrability [19]}, [20]}.
